november 2023 Schur- and Baer-type theorems for Lie and Leibniz algebras
Guram Donadze, Tim Van der Linden
Bull. Belg. Math. Soc. Simon Stevin 30(3): 386-398 (november 2023). DOI: 10.36045/j.bbms.230609

Abstract

The aim of this article is to obtain variations on the classical theorems of Schur and Baer on finiteness of commutator subgroups, valid in the contexts of Lie algebras and Leibniz algebras over a field. Using non-abelian tensor products and exterior products, we prove Schur's Theorem for finitely generated Leibniz algebras, both Schur's Theorem and Baer's Theorem for finitely generated Lie algebras, and a version of these theorems for finitely presented Lie algebras.

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Guram Donadze. Tim Van der Linden. "Schur- and Baer-type theorems for Lie and Leibniz algebras." Bull. Belg. Math. Soc. Simon Stevin 30 (3) 386 - 398, november 2023. https://doi.org/10.36045/j.bbms.230609

Information

Published: november 2023
First available in Project Euclid: 1 December 2023

Digital Object Identifier: 10.36045/j.bbms.230609

Subjects:
Primary: 17A32 , 17B55 , 18G10 , 18G45 , 18G50

Keywords: crossed module , homology , Leibniz algebra , Lie algebra , non-abelian tensor and exterior product

Rights: Copyright © 2023 The Belgian Mathematical Society

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Vol.30 • No. 3 • november 2023
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